GMAT Prep?? (Factors)

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

GMAT Prep?? (Factors)

by dferm » Thu May 08, 2008 5:26 am
The positive integers x,y, and z are such that x is a factor of y and y is a factor of z. Is z even?

(1) xz is even
(2) y is even


Can someone please help me here...?

Thanks.

Master | Next Rank: 500 Posts
Posts: 468
Joined: Sat Mar 03, 2007 10:17 pm
Thanked: 5 times

by moneyman » Thu May 08, 2008 5:41 am
Is it D?
Maxx

Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

by dferm » Thu May 08, 2008 7:04 am
Yes

User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

by AleksandrM » Thu May 08, 2008 9:43 am
The foundation rule here is that if x is a factor of y and y is a factor of z then x is also a factor of z. Now, you also know that y is bigger than x and z is either bigger than xy or equals to it.

Statement one tells you that xz is even. This means that one of the numbers is even. However, you also know that x is a factor of y. So if x is 3 and y is 9, then z MUST be even, or 18, for example. Sufficient.

Statement two tells you that y is even. If y is 6 and x is any odd integer, when you multiply them together, the result is always even. Now, z can have other factors, and all of them can be odd. As long as one of the factors is even, z MUST be even. Sufficient.

Choose D.

Senior | Next Rank: 100 Posts
Posts: 60
Joined: Sat May 30, 2009 11:22 am
Thanked: 2 times

by qwe12 » Tue Jul 28, 2009 2:38 am
let p and q be 2 constants

question says

p.x = y
q.y = z

q(p.x) = z
qp.x = z

let qp = some constant m

mx = z

now, evaluate the options

1) xz = even

(z/m).z = even

z.z = even * m
z.z = even

therefore z = even. SUFFICIENT

2) y = even

we know, q.y = z, q.even = even

so z = even. SUFFICIENT.

(D)